cp's OEIS Frontend

A118706 Triangular numbers whose digits in base 12 are contained in {1,5,7,11}.

%I A118706 #12 Aug 02 2024 08:57:30
%S A118706 1,91,1891,3403,403651,4388203,4468555,41710411,201553003,213283531,
%T A118706 410970115,428264011,633021571,642342403,703181251,4913725411,
%U A118706 28007409475,41103462403,90151709131,90294438403,337594212451,443352832075,1452321801451,1483280069635,4435473488491
%N A118706 Triangular numbers whose digits in base 12 are contained in {1,5,7,11}.
%C A118706 In base 12 all primes greater than 3 end in a 1, 5, 7, or E, where X is 10 and E is eleven. In base 12 the sequence is 1, 77, 1117, 1E77, 175717, 1577577, 15E5E77, 11E75E77, 575EE577, 5E517E77, E5771E17, EE511E77, 157EE7E17, 15E151E17, 1775E1717, E5171E117, 551775E717, 7E71571E17, 1557E75EE77, 155EE511E17, 55517751117, 71E11E71E77. Note that all elements after the first either end in 17 or 77. In base 12 the n such that t=n(n+1)/2 end in the digits 1 or X, but not respectively.
%F A118706 a(n) = t if t is the n-th triangular number such that S subset {1,5,7,11}, where S is the set of digits of t in base 12.
%F A118706 a(n) = A000217(A118711(n)). - _Amiram Eldar_, Aug 02 2024
%e A118706 a(4) = 3403 = 1E77 in base 12.
%p A118706 L:=[]: pd:={1,5,7,11}: for w to 1 do for n from 1 to 10^6 do t:=n*(n+1)/2; lod:=convert(t,base,12); sod:=convert(lod,set); if sod subset pd then L:=[op(L),[n,t]] fi; od od; L;
%t A118706 Select[Accumulate[Range[822000]],SubsetQ[{1,5,7,11},IntegerDigits[ #,12]]&] (* _Harvey P. Dale_, Oct 18 2019 *)
%Y A118706 Cf. A000217, A118711, A119033, A119034.
%K A118706 nonn,base
%O A118706 1,2
%A A118706 _Walter Kehowski_, May 24 2006
%E A118706 a(22)-a(25) from _Amiram Eldar_, Aug 02 2024